When a ceiling fan is switched on,it makes $10$ rotations in the first $3 \, s$. How many rotations will it make in the next $3 \, s$ (Assume uniform angular acceleration)?

$A$ small mass $m$ is attached to a massless string whose other end is fixed at $P$ as shown in the figure. The mass is undergoing circular motion in the $x-y$ plane with center $O$ and constant angular speed $\omega$. If the angular momentum of the system,calculated about $O$ and $P$ is denoted by $\vec L_o$ and $\vec L_p$ respectively,then:

Freundlich adsorption isotherms for the physical adsorption of a gas at temperatures $T_1$,$T_2$,and $T_3$ are shown in the graph given below. The correct relationship between $T_1$,$T_2$,and $T_3$ is:

$15 \text{ mL}$ of aqueous solution of $Fe^{2+}$ in acidic medium completely reacted with $20 \text{ mL}$ of $0.03 \text{ M}$ aqueous $Cr_2O_7^{2-}$. The molarity of the $Fe^{2+}$ solution is $.......... \times 10^{-2} \text{ M}$ (Round off to the Nearest Integer).

If the equation $ax^2 + 2hxy + by^2 + 2gx + 2fy + c = 0$ represents a pair of straight lines,then the square of the distance of their point of intersection from the origin is

The imperfect fungi which are decomposers of litter and help in mineral cycling belong to: